How (and why) to raise e to the power of a matrix | DE6
3Blue1Brown 3Blue1Brown
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 Published On Apr 1, 2021

General exponentials, love, Schrödinger, and more.
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Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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The Romeo-Juliet example is based on this essay by Steven Strogatz:
http://www.stevenstrogatz.com/essays/...

The book shown at the start is Vladimir Arnold's (excellent) textbook on ordinary differential equations.
https://amzn.to/3dtXSwj

Need a review of ordinary powers of e?
   • What's so special about Euler's numbe...  

Or of linear algebra?
   • Linear transformations and matrices |...  

Timetable
0:00 - Definition
6:40 - Dynamics of love
13:17 - Linear systems
20:03 - General rotations
22:11 - Visualizing with flow

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Code for this video:
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Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/

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https://vincerubinetti.bandcamp.com/a...

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https://open.spotify.com/album/1dVyjw...

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